Monte Carlo strategies for first-principles simulations of elemental systems

We discuss the application of atomistic Monte Carlo simulation based on electronic structure calculations to elemental systems such as metals and alloys. As in prior work in this area, an approximate "pre-sampling" potential is used to generate large moves with a high probability of acceptance. Even with such a scheme, however, such simulations are extremely expensive and may benefit from algorithmic developments that improve acceptance rates and/or enable additional parallelization. Here we consider several such developments. The first of these is a three-level hybrid algorithm in which two pre-sampling potentials are used. The lowest level is an empirical potential, and the "middle" level uses a low-quality density functional theory. The efficiency of the multistage algorithm is analyzed and an example application is given. Two other schemes for reducing overall run-time are also considered. In the first, the Multiple-try Monte Carlo algorithm, a series of moves are attempted in parallel, with the choice of the next state in the chain made by using all the information gathered. This is found to be a poor choice for simulations of this type. In the second scheme, "tree sampling," multiple trial moves are made in parallel such that if the first is rejected, the second is ready and can be considered immediately. Performance of this scheme is shown to be quite effective under certain reasonable run parameters.